of Heights by the Barometer. 407 



sing between the temperature and the density the relation 



f being a constant depending on the rate at which the tempera- 

 ture decreases as the height increases. 



For the purpose of comparison, I subjoin the following Table 

 of the successive densities according to the distances from the 

 earth's surface, as deduced from the various laws just mentioned. 



Table III. — Showing the Decrease of Density at different Alti- 

 tudes resulting from various laws. 



Height. 



Density of the air. 



Ob- Uniform 

 served, decrease. 



Difference. 



Bessel. 



Difference. 



Laplace. 



Difference. 



Ivory. 



Difference. 



feet. 

 



5,000 

 10,000 

 15,000 

 20,000 

 25,000 

 30,000 



10000 10000 

 0-8734 0-8867 

 7441 0-7734 

 6286 6601 

 05257 0-5468 

 0-4363 4335 

 3597 3202 



0000 

 +0013 3 

 +0 0293 

 + 0315 

 +0021 1 

 -0002 8 

 -00395 



10000 

 0-8367 

 07000 

 0-5857 

 04900 

 4100 

 0-3430 



00000 

 -0 0367 

 -00441 

 -0 0429 

 -00357 

 -0 0263 

 -00167 



1-0000 

 08649 

 0-7366 

 0-6188 

 05131 

 0-4205 

 0-3411 



0-0000 

 -00085 

 -0 0075 

 -0 0098 

 -00126 

 -00158 

 -00186 



1-0000 

 08714 

 7514 

 0-H434 

 0-5515 

 0-4681 

 03939 



0-0000 

 -00020! 

 +00073 

 +00148 

 +0-0258 

 +00318 

 + 0342 



Sum of the squares 1 

 of the differences J 



00040 





00074 





00010 





00031 



The column headed "Density of the air observed" is derived 

 from Table II. by means of interpolations in order to have the 

 altitudes in an arithmetical progression. The figures in the 

 third column were calculated by the formula 



Po 



ax, 



in which a, deduced by the method of least squares, was taken 



a = 000002266. 

 The densities resulting from the different hypotheses were calcu- 

 lated respectively by means of the following equations: — 



P_ _ e - (0-000035666)* 



Po 



Bessel's 



Laplace's . 



Ivory's 



£ = [1+ (661-107)w>-f 1348 -° 4 ^ 



Po / n\ 



^=(20886860> + 6138(1- -^-). 



P<y 



^=e- 

 Po 



#=(22384)^+14922 



(-£) 



